Explore advanced mathematical concepts at the intersection of spectral theory and general relativity through this comprehensive workshop series from the Erwin Schrödinger International Institute for Mathematics and Physics. Delve into cutting-edge research on spectral methods applied to gravitational physics, covering topics such as spectral theory of stationary spacetimes, stability questions in general relativity, and the mathematical foundations of quantum field theory and Hawking radiation. Learn from leading experts as they present lectures on semi-classical approximation for time-dependent systems, microlocal methods for operators with analytic coefficients, massive waves gravitationally bound to static bodies, and the nonlinear stability of Kerr-de Sitter spacetimes. Examine advanced topics including Feynman propagators on curved spacetimes, infrared finite scattering theory in quantum field theory and quantum gravity, Hadamard states for Maxwell fields, and renormalization group equations on curved spacetimes. Discover applications of spectral theory to wave equations in various spacetime geometries, index theory on Lorentzian manifolds, quasinormal modes of extremal black holes, and the mathematical analysis of cosmic censorship. Gain insights into the fundamental role of spectral theory in describing nature through quantum mechanics while exploring its influential applications across pure and applied mathematics in the context of Einstein's general relativity.

Syllabus

Clotilde Fermanian Kammerer - Semi-classical approximation for time-dependent systems
Jonathan Glöckle - Initial data rigidity via Dirac-Witten operators
Ethan Sussman - Massive waves gravitationally bound to static bodies
Maciej Zworski - Microlocal methods for operators with analytic coefficients I
Alexander Strohmaier - Spectral theory of stationary spacetimes I
Maciej Zworski - Microlocal methods for operators with analytic coefficients II
Alexander Strohmaier - Spectral theory of stationary spacetimes II
Maciej Zworski - Microlocal methods for operators with analytic coefficients III
Alexander Strohmaier - Spectral theory of stationary spacetimes III
Alexander Strohmaier - Spectral theory of stationary spacetimes IV
Maciej Zworski - Microlocal methods for operators with analytic coefficients IV
Maciej Zworski - Classically forbidden regions and analytic hypoellipticity
Allen Juntao Fang - Nonlinear stability of Kerr-de Sitter
Oliver Petersen - Wave equations in Kerr-de Sitter spacetimes: the full subextremal range
Onirban Islam - Feynman propagators on curved spacetime
Gautam Satishchandran - Infrared Finite Scattering Theory in QFT and Quantum Gravity
Alden Waters - The relative trace formula in electromagnetic scattering
Simone Murro - Hadamard states for Maxwell fields via complete gauge fixing
Kasia Rejzner - New proposal for renormalisation group equations on curved spacetimes
Robert Wald - Quantum Field Theory in Curved Spacetime
Dean Baskin - The Feynman propagator for the wave equation with an inverse square potential
András Vasy - The Feynman propagator and self-adjointness
Semyon Dyatlov - Microlocal analysis of internal waves in 2D aquaria
Jeremy L. Marzuola - Spectral minimal partitions, nodal deficiency and the Dirichlet-to-Neumann map
Jonathan Luk - Late time tail of waves on dynamic asymptotically flat spacetimes...
Christian Bär - Survey on Index Theory on Lorentzian Manifolds
Stefan Czimek - Obstruction-free gluing for the Einstein equations
Christoph Kehle - A small divisors instability at the Kerr-AdS Cauchy horizon
Claude Warnick - Quasinormal modes of (near) extremal black holes
Claudio Dappiaggi - Fundamental solutions and Hadamard states for a scalar field with arbitrary...
Jared Wunsch - Wave propagation on rotating cosmic string backgrounds
Stefan Hollands - Semi-classical analysis of strong cosmic censorship
Colin Guillarmou - Virasoro semi-groups and conformal blocks